Find all sollutions of the equation 4 sin2x 3 0 on the int

Find all sollutions of the equation 4 sin^2(x) - 3 = 0 on the interval [0, 2pi) The answer is A, B, C, and D. where 0

4sin^2x -3 =0 Interval [0, 2pi )

sin^2(x) = 3/4

sinx = +/- sqrt(3)/2

sin = sqrt3/2 ----> x = sin^-1(sqrt(3)/2)

sin is +ve in Ist and IIndquadrant: So,

A = pi/3 ; B = 2pi/3

sin = - sqrt3/2 -----> sin is -ve in IIIrd and IVrth quadrant

C= pi +pi/3 = 4pi/3

D = 2pi -pi/3 = 5pi/3